Fourier-transform ion cyclotron resonance (FT-ICR) mass analyzers measure mass-to-charge ratios (m/z) of ions indirectly, based on an image current generated by ions moving within a magnetic field of a Penning Trap at their respective cyclotron frequencies. The resulting signal is a time-decaying interferogram known as a transient, defined over the domain of time, that consists of multiple superposed sine waves. The individual frequencies of which the transient is composed may be determined by calculation of a Fourier Transform of the transient signal. The m/z values of the various ion species are calculated from the frequencies.
Electrostatic traps are a different class of mass analyzer in which moving ions experience multiple reflections or deflections in substantially electrostatic fields. In similarity to FT-ICR mass analyzers, electrostatic trap mass analyzers likewise generate a discernible signal by measurement of an image current (i.e., a transient) that is induced within electrodes of the electrostatic by the periodic motion of ion species within the trap. Two known types of electrostatic trap mass analyzers are Cassinian trap mass analyzers (discussed further below) and ORBITRAP™ mass analyzers.
The ORBITRAP™ mass analyzer, which is commercially available from Thermo Fisher Scientific of Waltham Mass. USA, is one such electrostatic trap that has become widely recognized as a useful tool for mass spectrometric analysis. FIGS. 1A and 1B, discussed further below, provide schematic illustrations of an ORBITRAP™ mass analyzer. The main advantages of electrostatic trapping mass analyzers such as Cassinian trap and ORBITRAP™ mass analyzers and of mass spectrometer systems that incorporate them are that they provide accurate mass-to-charge (m/z) measurements and high m/z resolution similar to what is achievable with Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry instrumentation but without the requirement for a high-strength magnet. Structural and operational details of ORBITRAP™ mass analyzers and mass spectrometers employing such mass analyzers are described in Makarov, Electrostatic Axially Harmonic Orbital Trapping: A High-Performance Technique of Mass Analysis, Anal. Chem., 72(6), 2000, pp. 1156-1162 and in U.S. Pat. No. 5,886,346 in the name of inventor Makarov and in U.S. Pat. No. 6,872,938 in the names of inventors Makarov et al.
In both FT-ICR and electrostatic trap mass analyzers, ions are compelled to undergo collective oscillatory motion within the analyzer which induces a correspondingly oscillatory image charge in neighboring detection electrodes, thereby enabling detection of the ions. The oscillatory motion used for detection may be of various forms including, for example, circular oscillatory motion in the case of FT-ICR mass analyzers and axial oscillatory motion while orbiting about a central electrode in the case of mass analyzers of the type illustrated in FIGS. 1A-1B. The oscillatory image charge in turn induces an oscillatory image current and corresponding voltage in circuitry connected to the detection electrodes, which is then typically amplified, digitized and stored in computer memory which is, as noted above, referred to as a transient (i.e. a transitory signal in the time domain).
The component frequencies of the transient, as generated by either an FT-ICR apparatus or an electrostatic trap apparatus are related to the mass-to-charge (m/z) values of the ions. Each ion of a given mass to charge (m/z) value will oscillate at a corresponding given frequency such that it contributes a signal to the collective ion image current which is generally in the form of a periodic wave at the given frequency. The total detected image current of the transient is then the resultant sum of the image currents at all the frequencies present (i.e. a sum of periodic signals). Signal frequency analysis (such as Fourier transformation) of the transient yields the oscillation frequencies, where each such frequency is associated with a particular detected ion species. The m/z values of the ions can then be determined (i.e. the mass spectrum) from the frequencies by known equations with parameters determined by prior calibration experiments.
More specifically, an ORBITRAP™ mass analyzer includes an outer barrel-like electrode and a central spindle-like electrode along the axis. Referring to FIG. 1A, a portion of a mass spectrometer system including an ORBITRAP™ mass analyzer is schematically shown in longitudinal section view. The mass spectrometer system 1 includes an ion injection device 2 and an electrostatic orbital trapping mass analyzer 4. The ion injection device 2, in this case, is a curved multipolar curvi-linear trap (known as a “C-trap”). Ions are ejected radially from the “C-trap” in a pulse to the electrostatic trap. For details of the curved trap, or C-trap, apparatus and its coupling to an electrostatic trap, please see U.S. Pat. Nos. 6,872,938; 7,498,571; 7,714,283; 7,728,288; and 8,017,909 each of which is hereby incorporated herein by reference in its entirety. The C-trap may receive and trap ions from an ion source 3 which may be any known type of source such as an electrospray (ESI) ion source, a Matrix-Assisted Laser Desorption Ionization (MALDI) ion source, a Chemical Ionization (CI) ion source, an Electron Ionization (EI) ion source, etc. Additional not-illustrated ion processing components such as ion guiding components, mass filtering components, linear ion trapping components, ion fragmentation components, etc. may optionally be included (and frequently are included) between the ion source 3 and the C-trap 2 or between the C-trap and other parts of the mass spectrometer. Other parts of the mass spectrometer which are not shown are conventional, such as additional ion optics, vacuum pumping system, power supplies etc.
Other types of ion injection devices may be employed in place of the C-trap. For example, the aforementioned U.S. Pat. No. 6,872,938 teaches the use of an injection assembly comprising a segmented quadrupole linear ion trap having an entrance segment, an exit segment, an entrance lens adjacent to the entrance segment and an exit lens adjacent to the exit segment. By appropriate application of “direct-current” (DC) voltages on the two lenses as well as on the rods of each segment, a temporary axial potential well may be created in the axial direction within the exit segment. The pressure inside the trap is chosen in such a way that ions lose sufficient kinetic energy during their first pass through the trap such that they accumulate near the bottom of the axial potential well. Subsequent application of an appropriate voltage pulse to the exit lens combined with ramping of the voltage on a central spindle electrode causes the ions to be emptied from the trap axially through the exit lens electrode and to pass into the electrostatic orbital trapping mass analyzer 4.
The electrostatic orbital trapping mass analyzer 4 comprises a central spindle shaped electrode 6 and a surrounding outer electrode which is separated into two halves 8a and 8b. FIG. 1B is an enlarged cross-sectional view of the inner and outer electrodes. The annular space 17 between the inner spindle electrode 6 and the outer electrode halves 8a and 8b is the volume in which the ions orbit and oscillate and comprises a measurement chamber in that the motion of ions within this volume induces the measured signal that is used to determine the ions m/z ratios and relative abundances. The internal and external electrodes (electrodes 6 and 8a, 8b) are specifically shaped such that, when supplied with appropriate voltages will produce respective electric fields which interact so as to generate, within the measurement chamber 17, a so-called “quadro-logarithmic potential”, U, (also sometimes referred to as a “hyper-logarithmic potential”) which is described in cylindrical coordinates (r, z) by the following equation:
                    U        =                                            a              2                        ⁢                          (                                                z                  2                                -                                                      r                    2                                    2                                            )                                +                      b            ⁢                          ln              ⁡                              (                                  r                  c                                )                                              +          d                                    Eq        .                                  ⁢        1            where a, b, c, and d are constants determined by the dimensions of and the voltage applied to the orbital trapping analyzer electrodes, where z=0 is taken at the axial position corresponding to the equatorial plane of symmetry 7 of the electrode structure and chamber 17 as shown in FIG. 1B. The “bottom” or zero axial gradient point of the portion of “quadro-logarithmic potential” dependent on the axial displacement (i.e. the portion which determines motion in the axial dimension, z, along the longitudinal axis 9) occurs at the equatorial plane 7. This potential field has a harmonic potential well along the axial (Z) direction which allows an ion to be trapped axially within the potential well if it does not have enough kinetic energy to escape. It should be noted that Eq. 1 represents an ideal functional form of the electrical potential and that the actual potential in any particular physical apparatus will include higher-order terms in both z and r.
The motions of trapped ions within an electrostatic trap of the type illustrated in FIGS. 1A-1B are associated with three characteristic oscillation frequencies: a frequency of rotation around the central electrode 6, a frequency of radial oscillations a nominal rotational radius and a frequency of axial oscillations along the z-axis. In order to detect the frequencies of oscillations, the motion of ions of a given m/z need to be coherent. The radial and rotational oscillations are only partially coherent for ions of the same m/z as differences in average orbital radius and size of radial oscillations correspond to different orbital and radial frequencies. It is easiest to induce coherence in the axial oscillations as ions move in an axial harmonic potential so axial oscillation frequency is independent of oscillation amplitude and depends only on m/z and, therefore, the axial oscillation frequencies are the only ones used for mass-to-charge ratio determinations. The outer electrode is formed in two parts 8a, 8b as described above and is shown in FIG. 1B. The ions oscillate sinusoidally with a frequency, ω, (harmonic motion) in the potential well of the field in the axial direction according to the following Eq. 2:
                    ω        =                              k                          (                              m                /                z                            )                                                          Eq        .                                  ⁢        2            where k is a constant. One or both parts 8a, 8b of the outer electrode are used to detect image current as the ions oscillate back and forth axially. The Fourier transform of the induced ion image current signal from the time domain to the frequency domain can thus produce a mass spectrum in a conventional manner. This mode of detection makes possible high mass resolving powers.
Ions having various ink values which are trapped within the C-trap are injected from the C-trap into the electrostatic orbital trapping mass analyzer 4 in a temporally and spatially short packet at an offset ion inlet aperture 5 that is located at an axial position which is offset from the equatorial plane 7 of the analyzer in order to achieve “excitation by injection” whereby the ions of the ion packet immediately commence oscillation within the mass analyzer in the quadro-logarithmic potential. The ions oscillate axially between the two outer electrodes 8a and 8b while also orbiting around the inner electrode 6. The axial oscillation frequency of an ion is dependent on the ink values of the ions contained within the ion packet so that ions in the packet with different ink begin to oscillate at different frequencies.
The two outer electrodes 8a and 8b serve as detection electrodes. The oscillation of the ions in the mass analyzer causes an image charge to be induced in the electrodes 8a and 8b and the resulting image current in the connected circuitry is picked-up as a signal and amplified by an amplifier 10 (FIG. 1A) connected to the two outer electrodes 8a and 8b which is then digitized by a digitizer 12. The resulting digitized signal (i.e. the transient) is then received by an information processor 14 and stored in memory. The memory may be part of the information processor 14 or separate, preferably part of the information processor 14. For example, the information processor 14 may comprise a computer running a program having elements of program code designed for processing the transient. The computer 14 may be connected to an output means 16, which can comprise one or more of: an output visual display unit, a printer, a data writer or the like.
The transient received by the information processor 14 represents the mixture of the image currents produced by the ions of different ink values which oscillate at different frequencies in the mass analyzer. A transient signal for ions of one ink is periodic as shown in FIG. 2A, which shows a “symbolic” approximately sinusoidal transient 21 for just a few oscillations of a single frequency (m/z) component. A representative transient 22 obtained when several different frequencies are combined is shown in FIG. 2B. The m/z value of the ion determines the period (and frequency) of the periodic function. The Single Transient Signal (STS) for single frequency component corresponding to oscillation of ions having mass-to-charge ratio (m/z)1 is approximated by:STS=A sin(2πωt+φ0)  Eq. 3where A is a measure of the abundance (quantity) of ions having mass-to-charge ratio (m/z)1 in the trap, ω is the frequency, t is time and φ0 is the initial phase (at t=0). This equation is only an approximation because it does not account for decay of the amplitude and loss of coherence over time.
The information processor 14 performs a mathematical transform on the received transient in order to derive information relating to the various component STS signals. The mathematical method of discrete Fourier transformation may be employed to convert the transient in the time domain (e.g., curve 22 in FIG. 2B) into a spectrum in the frequency domain. If desired, at this stage or later, the frequency domain spectrum can be converted into the m/z domain by straightforward calculation or calibration. The discrete Fourier transformation produces a spectrum which has a profile point for each frequency or m/z value, and these profile points comprise a peak at those frequency or m/z positions where an ion signal is detected (i.e. where an ion of corresponding m/z is present in the analyzer). Although Fourier Transform methods and algorithms (such as the discrete Fourier transform (DFT) and the fast Fourier transform (FFT)) are often employed to extract information from a transient signal, other mathematical transform procedures may alternatively be employed for the same purpose.
Generally stated, a Cassinian electrostatic ion trap comprises an outer electrode with an ion-repelling electric potential and at least two inner electrodes with ion-attracting potentials, where the outer electrode and the inner electrodes are shaped and arranged in such a way that a harmonic electric potential is formed in one spatial direction and, perpendicular to this spatial direction, an electric potential is formed in which ions move on stable, radial trajectories. For example, a known Cassinian electrostatic ion trap, as described in U.S. Pat. No. 7,994,473, comprises an outer electrode maintained at a first electrical potential and two spindle-shaped inner electrodes both maintained at a same second electrical potential. Together, the outer electrode and inner spindle electrodes generate an electric potential, U, between the electrodes that takes the form of Eq. 4:
                              U          ⁡                      (                          x              ,              y              ,              z                        )                          =                              U            0                    +                                    U              C                        ⁢                          ln              ⁡                              [                                                                                                    (                                                                              x                            2                                                    +                                                      y                            2                                                                          )                                            2                                        -                                          2                      ⁢                                                                        b                          2                                                ⁡                                                  (                                                                                    x                              2                                                        -                                                          y                              2                                                                                )                                                                                      +                                          b                      4                                                                            a                    4                                                  ]                                              -                                    k              2                        ⁢                          (                                                x                  2                                +                                  y                  2                                            )                                +                      k            ⁢                          z              2                                                          Eq        .                                  ⁢        4            where, x, y and z are Cartesian coordinates, U0 is an offset of the potential that is proportional to the voltage between the outer electrode and the inner electrodes, UC is a scaling factor, and where a, b and k are parameters (constants). The outer electrode and the two spindle-shaped inner electrodes are shaped and arranged such that the inner surface of the outer electrode and the surfaces of the spindle-shaped inner electrodes each correspond to equipotential surfaces of the above electric potential. Accordingly, each spindle electrode is shaped with a diameter that is greatest at its central region and that tapers towards each end. The parameters a and b are related to the radial geometry of the electrode system. The parameter b, which is non-zero, corresponds to the distance between the axis of each spindle and the central z-axis. The parameter k determines the harmonic motion of the ions along the z-axis and is also proportional to the voltage between the outer electrode and the inner electrodes. Specifically, The parameter k, the ion mass m, and the charge z of the ion determine the oscillation frequency ω of the harmonic oscillation along the z-direction:
                    ω        =                                            2              ⁢              k                                      m              /              z                                                          Eq        .                                  ⁢        5            
As noted in the aforementioned U.S. Pat. No. 7,994,473, one way to obtain mass-dependent data from such a Cassinian electrostatic ion trap is to measure the oscillation frequency of ions along the z-direction. Each ion package oscillating inside the Cassinian electrostatic ion trap induces a periodic signal in an ion detector, which is electronically amplified and measured as a function of time. The ion detector comprises detection elements, such as detection coils, in which ion packages induce voltages as they fly through, or detection electrodes, for example segments of the outer electrode or inner electrodes, in which ion packages induce image charges as they fly past. Thus, in analogy to data acquisition procedures employed during operation of an ORBITRAP™ orbital trapping electrostatic trap, a Fourier transform (or other mathematical transform procedure) can be used to transform a measured time signal of z-axis oscillations into a frequency spectrum, which can be converted into a mass spectrum via the known mass dependence of the z-axis oscillation frequency.
The aforementioned U.S. Pat. No. 7,994,473 teaches that ions may be preferably introduced into a Cassinian electrostatic ion trap of the type described above by introduction of the ions into the plane of symmetry (the medial y-z plane) between the two inner electrodes. Upon introduction, such ions begin oscillations parallel to at least the y-axis. Further, if the ions are introduced into the medial y-z plane at a z-axis coordinate that is not at the minimum of the z-axis harmonic potential, they will also immediately start to oscillate along the z-axis. If, however, the ions may are quasi-continuously introduced directly at the potential minimum of the harmonic potential, the ions move with only small amplitudes along the z-axis according to their initial energy in z-direction. After the ions are introduced and stored in the potential minimum in this fashion, they are excited to harmonic oscillations, for example by using a high frequency electric dipole field along the z-axis.
In both the ORBITRAP™ electrostatic orbital trapping mass analyzer and the Cassinian electrostatic ion trap mass analyzer, the z-axis oscillations are mathematically separable from other oscillations and may be mathematically treated as simple harmonic oscillation parallel to the z-axis, wherein an apparent minimum in the z-axis harmonic potential occurs at a central plane of symmetry of the apparatus. In operation of either apparatus, this apparent simple harmonic motion parallel to the z-axis is used to advantage in order to obtain m/z-dependent data which may be used for the purpose of mass analysis.
The resolution of mass spectra acquired with an FT-ICR or electrostatic trap mass analyzer is determined by the so-called “transient length”, which is the time during which an image current signal is recorded before the transient data is converted into an m/z spectrum by means (generally) of a Fourier Transform calculation. An increased transient length correlates to greater mass spectral resolution. For example, to achieve a mass spectral resolution of 15000 at an m/z of 200 Th, a transient length of only 32 ms is required whereas the achievement of a mass spectral resolution of 500,000 at the same m/z requires a transient length of greater than 1000 ms.
FIGS. 3A-3B illustrate how mass spectra change with changing settings of resolution. FIG. 3A is a set of three experimental measurements of a portion of the mass spectrum of the fungicide pyrimethanil acquired at resolutions of 15000 (trace 301), 30000 (trace 302) and 60000 (trace 304). At a resolution of 60000, the pyrimethanil peak 307 at 199.11026 Th is fully resolved from the peak 305 of an interfering ion (from the sample matrix) at 199.10570 Th. However, the two peaks merge at resolutions of 30000 and below. At these lower resolution settings, the presence of the interfering ion shifts the centroid of the composite peak to lower m/z values, thereby reducing mass accuracy, and increases the total area under the trace in the region between 100.10 Th to 199.12 Th, thus affecting quantitative analysis. The lack of full resolution of the analyte peak at these lower resolution settings and in the presence of the interfering ion species may therefore lead to a failure to recognize the presence of the analyte in the sample or, otherwise, to an overestimate of its abundance it its presence is recognized.
FIG. 3B is a set of portions of the mass spectrum of sample of 13C and 15N labeled adenosine triphosphate (ATP; C10H16N5O13P3) acquired at different resolutions. In sequence, the rows of spectra from top to bottom correspond to resolution settings of 15000, 30000, 60000, 120000 and 240000, respectively. Note that the nominal isobaric m/z of the non-labeled analyte is 508.00302 Th. Accordingly, the first column of spectra, comprising spectra 310-318, correspond to the +3 isotope lines, as obtained at the resolutions noted above. Likewise, the middle column of spectra, comprising spectra 310-318 correspond to the +5 isotope lines and the third column of spectra, comprising spectra 320-328 correspond to the +6 isotope lines. At resolutions of 30000 and below, the isotopic fine structure, representing differing ratios of carbon-to-nitrogen isotope substitution, remain indistinguishable from one another within each of the +3, +5 and +6 envelopes. With increasing resolution however, the emergence of separated peaks becomes increasingly apparent, with partial resolution first becoming evident in the +3 isotope lines at a resolution of 60000 and later becoming evident in the case of greater numbers of isotopic substitutions. Finally, at a resolution of 240000, peaks attributable to different ion species are well resolved.
In practice, it can be difficult to choose an appropriate mass resolution for operating an electrostatic trap mass analyzer of the type illustrated in FIGS. 1A-1B, depending on many factors, such as the degree to mass spectral lines of background substances occur in the vicinity of expected target m/z values, the amount of time available for making each measurement, the abundance of expected analytes, etc. If the resolution is too low, the analyte signal is compromised. On the other hand, if the resolution is too high, the number of mass spectral data acquisitions that may be made of one or more given analyte peak is unnecessarily reduced. Thus, an instrument operator must often make an estimate of a best mass spectral resolution to employ during mass spectral analysis of a sample, based on prior experience with similar samples. Once a resolution is so chosen, the quality of an entire mass spectral run depends on the appropriateness of the operator's choice. Therefore, there in a need in the art of Fourier-Transform mass spectrometry for systematic methods for choosing an appropriate mass spectral resolution setting for any sample and, especially, for choosing an appropriate resolution for a set of measurements while those measurements are in progress. The present invention addresses this need.